To report back about our current stay:
Staying at the villa's is like staying in a different hotel... amazing room. The people who work in The Villa Lounge are very attentive.
Apparently, something had to be fixed before we could enter the villa, so we had to wait one hour after check-in time.
I asked about a late check-out and they gave us a late check-out until 4 PM. Happy with this outcome, as our flight is at 8 PM.